What is the reason forth fourth and eighth steps in the proof?

You and a friend went to the movies.you spent half your money on tickets. then you spent 1/4 of the money on popcorn, $2 on candy, and $3 on a soda. if you have $1 left, hiw much money did u take to the movies?

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

I’m really confused and need your assist me with this question i’ve never been taught